# Math Help - Probability Q

1. ## Probability Q

Um, here I have a Probability Question, but I'm not completely sure where to even begin:

Given that the pass rate of an entrance exam for a Mathematics program is 55%, what is the probability that a student fails it the first two times and passes it the third time?

2. Originally Posted by NotoriousPi
Um, here I have a Probability Question, but I'm not completely sure where to even begin:

Given that the pass rate of an entrance exam for a Mathematics program is 55%, what is the probability that a student fails it the first two times and passes it the third time?
Assuming the probability that the student passes on any given taking of the test is 0.55, the answer is just (0.45)(0.45)(0.55) = 0.111375.

3. Wait why is that? I'm not quite sure I follow you here..

4. Originally Posted by NotoriousPi
Wait why is that? I'm not quite sure I follow you here..
It is joint probability of independent events. See here. Probability that he fails first test is 1-0.55 = 0.45. Probability of failing second test is again 0.45. Probability of passing third test is 0.55. Multiply them. Note that I assumed at the beginning that the events are independent.